Question

.Express 0.13333….. as a rational number.​

Answer 1

Answer:

1/5 is the answer

Step-by-step explanation:

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Answer 2

Solution :

Let $\mathtt{x = 0.1 \bar 3}$

Then, $\mathtt{x = 0.133333...}$ (i)

$\begin {gathered} \end {gathered}$

Since the repeating block has only a Digit, we Multiply x by 10 to get -

$\mathtt{10x = 1.33333...}$ (ii)

$\begin {gathered} \end {gathered}$

Subtracting (i) from (ii), we get -

$\begin {aligned} 9x = 1.2\: or\: \Big (\dfrac{12}{10}\Big )\Leftrightarrow \bold x &= \dfrac{12}{10} \div 9\\\\&\Rightarrow \dfrac{12}{10} \times \dfrac{1}{9} = \underline {\boxed {\bf \dfrac{12}{90}}} \end {aligned}$

$\begin {gathered} \end {gathered}$

Hence, $\boxed {\mathtt{0.1 \bar 3 = \dfrac{12}{90}}}$

$\begin {gathered} \end {gathered}$

Additional Information :

Rational Numbers:

The Numbers of the form $\mathtt{\dfrac{p}{q}}$, where p and q are integers and $\mathtt{q \neq 0}$, are known as Rational Numbers.

$\begin {gathered} \end {gathered}$

For Example, $\mathtt {\dfrac{1}{4}, \dfrac{3}{2}, \dfrac{11}{79}, -\dfrac{2001}{2002}, etc...}$ are all Rational Numbers.